Prime p₀= 2056695670407587939 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 124 2 28 2 10 2 40 2 34 2 (?)
a_n: 0 2 42 44 168 170 198 200 210 212 252 254 288 290
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 290
Found by: MarkRBright
db: batch=80, k=14, 40 124 28 10 40 34

SPT(16)	2056694193029757097	0 4 40 46 70 76 84 94 126 136 144 150 174 180 216 220	-1477377830842
STPT(10)	2056694404459167269	0 2 18 20 30 32 42 44 60 62	-1265948420670
STPT(10)	2056694764252736297	0 2 42 44 132 134 222 224 264 266	-906154851642
SPT(16)	2056695163659137317	0 4 42 60 112 136 180 184 222 226 270 294 346 364 402 406	-506748450622
SPT(16)	2056695357701025259	0 28 40 70 78 138 142 168 184 210 214 274 282 312 324 352	-312706562680
STPT(10)	2056695531516872579	0 2 12 14 90 92 168 170 180 182	-138890715360
STPT(10)	2056695671781472607	0 2 30 32 72 74 114 116 144 146	1373884668
SPT(16)	2056695950349818473	0 28 120 160 166 216 264 274 300 310 358 408 414 454 546 574	279942230534
SPT(16)	2056696110072655339	0 22 52 82 112 124 144 162 172 190 210 222 252 282 312 334	439665067400
SPT(16)	2056696145296997683	0 24 30 40 90 100 118 136 198 216 234 244 294 304 310 334	474889409744
SPT(16)	2056696347750465853	0 4 54 60 78 94 148 168 190 210 264 280 298 304 354 358	677342877914